The problem is with Mail.app (not Google Sync), which does not suport ActiveSync. It uses Exchange Web Services instead, which must be pulled.

The options for push in Mountain Lion appear to be either use Outlook 2011, which does use ActiveSync, or configure Mail.app to use IMAP. GMail supports IMAP IDLE, which is the IMAP equivalent of ActiveSync push.

"must be pulled" meaning that Microsoft announced that it's deprecated?
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YarJan 21 at 21:56

@Yar Meaning that the client must "pull" via polling, rather than "pushed" on-demand like ActiveSync. To my knowledge it's not deprecated, since it's alive and well in iOS. It seems like it should be possible to allow push-style web services via web sockets, but I have had trouble finding details.
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wstJan 22 at 0:42